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Hirota-sato formalism on some nonlinear waves equations

Ali, Noor Aslinda and Abdul Aziz, Zainal (2013) Hirota-sato formalism on some nonlinear waves equations. Jurnal Teknologi (Sciences and Engineering), 61 (1). pp. 1-6. ISSN 0127-9696

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Official URL: http://dx.doi.org/10.11113/jt.v61.1615

Abstract

This article demonstrates that Hirota’s direct method or scheme for solving nonlinear waves equation is linked to Sato theory, and eventually resulted in the Sato equation. This theoretical framework or simply the Hirota–Sato formalism also reveals that the τ – function, which underlies the analytic form of soliton solutions of theses physically significant nonlinear waves equations, shall acts as the key function to express the solutions of Sato equation. From representation theory of groups, it is shown that the τ – function in the bilinear forms of Hirota scheme are closely connected to the Plucker relations in Sato theory. Thus Hirota–Sato formalism provides a deeper understanding of soliton theory from a unified viewpoint. The Kadomtsev–Petviashvili (KP), Korteweg–de Vries (KdV) and Sawada–Kotera equations are used to verify this framework

Item Type:Article
Uncontrolled Keywords:Hirota–Sato formalism, τ – function, Plucker relations; Kadomtsev–Petviashvili (KP) equation, Korteweg–de Vries (KdV) equation, Sawada–Kotera equation
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:50007
Deposited By: Siti Nor Hashidah Zakaria
Deposited On:02 Dec 2015 10:10
Last Modified:14 Oct 2018 16:26

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